The moment of inertia of a thin uniform rod of mass M and length L about an axis passing through its midpoint and perpendicular to its length is `I_(0)`. Its moment of inertia about an axis passing through one of its ends and perpendicular to its length is .............

Options

A. `I_(0)+(ML^(2))/(2)`
B. `I_(0)+(ML^(2))/(4)`
C. `I_(0)+2ML^(2)`
D. `I_(0)+ML^(2)`

Answer

B

Explanation

The moment of inertia about the middle axis is `I_(0)`, Now according to parallel axis
`I=I_(0)+Md^(2)`
putting `d=(L)/(2)`
`I=I_(0)+M((L)/(2))^(2)`
`therefore I=I_(0)+(ML^(2))/(4)`